Self-calibration of three-legged modular reconfigurable parallel robots based on leg-end distance errors

A class of three-legged modular reconfigurable parallel robots is designed and constructed for precision assembly and light machining tasks by using s tandard active and passive joint modules in conjunction with custom designe d Links and mobile platforms. Since kinematic errors, especially the assemb ly errors, are likely to be introduced, kinematic calibration becomes parti cularly important to enhance the positioning accuracy of a modular reconfig urable robot. Based on the local frame representation of the Product-Of-Exp onentials (Local POE) formula, a self-calibration method is proposed for th ese three-legged modular reconfigurable parallel robots. In this method, bo th revolute and prismatic joint axes can be uniformly expressed in twist co ordinates by their respective local (body) frames. Since these local frames can be arbitrarily defined on their corresponding links, we are able to ca librate them, and yet retain the nominal local description of their respect ive joints, i.e., the nominal twist coordinates and nominal joint displacem ents, to reflect the actual kinematics of the robot. The kinematic calibrat ion thus becomes a procedure of fine-tuning the locations and orientations of the local frames. Using mathematical tools from differential geometry an d group theory, an explicit linear calibration model is formulated based on the leg-end distance errors. An iterative least-square algorithm is employ ed to identify the error parameters. A simulation example of calibrating a three-legged (RRRS) modular parallel robot shows that the robot kinematics can be fully calibrated within two to three iterations.